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4 papers
Local elliptic law
Johannes Alt, Torben Krüger
The empirical eigenvalue distribution of the elliptic random matrix ensemble tends to the uniform measure on an ellipse in the complex plane as its dimension tends to infinity. We…
Inhomogeneous Circular Law for Correlated Matrices
Johannes Alt, Torben Krüger
We consider non-Hermitian random matrices with general decaying correlations between their entries. For large , the empirical spectral distributi…
Cusp Universality for Random Matrices II: The Real Symmetric Case
Giorgio Cipolloni, László Erdős, Torben Krüger +1
We prove that the local eigenvalue statistics of real symmetric Wigner-type matrices near the cusp points of the eigenvalue density are universal. Together with the companion paper…
The Dyson equation with linear self-energy: spectral bands, edges and cusps
Johannes Alt, Laszlo Erdos, Torben Krüger
We study the unique solution of the Dyson equation \[ -m(z)^{-1} = z - a + S[m(z)] \] on a von Neumann algebra with the constraint . Here, $…